It is the perfect way to introduce audiences to a new band: screen a heartwarming full-length movie about them first. When the Orchestra di Piazza Vittorio troop on afterwards for their UK debut, the audience greet them like old friends.

Back in 2001, pianist Mario Tronco decided to form a world music orchestra. Film-maker Agostino Ferrente follows Tronco as he goes on a mission to recruit musicians in Rome's multicultural Esquilino district. Argentine percussionist Raul "Cuervo" Scebba, based in a lock-up garage, gets it straight away: "You mean like the Blues Brothers," he says with a smile.

But the film is closer in tone to The Commitments, as we encounter some great characters: charming Senegalese percussionist Pap; charismatic Tunisian singer Houcine Ataa; Carlos Paz, who we see playing Andean flutes for tourists. Against all odds – indifference, language barriers, money troubles, Italian bureaucracy – the orchestra give their first concert late in 2002. It is hard not to shed a tear as more than a dozen nationalities and languages unite in music.

As the screening ends, the band kick off, and the engagingly shaggy Tronco, who has broken an elbow, is given a hero's welcome; he spends most of his time conducting and leaping around. When Ataa enters to sing Sahara Blues he is greeted with huge cheers, as is Paz with his wordless Tarareando. There are several new, equally riveting performers in the mix, including Dialy Mady Sissoko on the kora, and the Brazilian guitarist Evandro Cesar Dos Reis.

Reminiscent of London's Grand Union but with an Italian flavour, they move effortlessly between genres and grooves: from pumping Arabic disco through Latin showstoppers to the storming, string-led "Philly soul" of Ena Andi. But there is a surprise in the encore: two extracts from their ambitious reinterpretation of Mozart's Magic Flute, an improbable confection that is every bit as joyful as the movie.